List of top Mathematics Questions asked in KEAM

The standard deviation of a data set \( x_1, x_2, \dots, x_6 \) (\( x_i>0 \)) is 2. If \[ \sum_{i=1}^{9} x_i^2 = 360, \] then the mean of the data set is
The means of two samples of size 30 and 40 are 35 and 42 respectively. Then the mean of the combined sample of size 70 is
If \[ A = \begin{bmatrix} -7 & 3 \\ 3 & -1 \end{bmatrix} \] then \( \det(A^5) \) is equal to:
Let \( A \) be a \( 3 \times 3 \) matrix with \( |A| = 7 \). If \( B = 3A \), then the value of \[ \left| \frac{{adj } A}{B} \right| \] is equal to
The value of the sum \[ \sum_{k=0}^{48} \frac{1}{(k + 1)(k + 2)} \] is equal to
The relation \( R \) in the set of integers \( \mathbb{Z} \) is given by \( R = \{(a, b) : b = 2a + 3 \} \). Then the relation \( R \) is:
Let \( A = \{ 1, 3, 5, 7, \dots, 21 \} \). The number of ways 4 numbers, containing always 11, can be selected from the set A is equal to
The sum of the first 20 terms of the G.P. \( \sqrt{3} + \frac{-1}{\sqrt{3}} + \frac{1}{3\sqrt{3}} + \cdots \) is equal to
The number of positive integers that have at most seven digits and contain only the digits 0 and 9 is
If the complex number \( 2 + i \) is rotated through an angle \( 90^\circ \) in the anti-clockwise direction about the origin in the complex plane, then the resulting complex number is
Let \( z = x + iy \), where \( y>0 \). If \( z + \overline{z} = 6 \) and \( |z| + | \overline{z} | = 10 \), then \( z = \)
If the complex number \( \frac{2 + i}{\lambda + i} \) lies on the line \( y = x \) of the first quadrant, then the value of \( \lambda \) is equal to
Let \( f(x) = 6x^2 + 9x + 10 \) and \( g(x) = x^2 - 9x - 9 \). Then the value of \( (f \circ g)(10) \) is
If \( x \) satisfies the inequality \( -3<\frac{1}{2} + \frac{-3x}{2} \leq 6 \), then \( x \) lies in the interval
The range of the function \( f(x) = 8 + \sqrt{x - 5} \) is:

Let \( f(x) = \sqrt{4 - x^2} \), \( g(x) = \sqrt{x^2 - 1} \). Then the domain of the function \( h(x) = f(x) + g(x) \) is equal to:

The number of solutions of the equation \( \dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}\) is 
The value of λ for which the vectors \(2i-3j+4k\) and \(-4i+λj-8k\) are collinear is 
A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?

Let \(S=\){\(n∈NIn^3+3n^2+5n+3\) is not divisible by \(3\)}.Then, which of the following statements is true about \(S\)

The value of \(cos^{-1}(cos(\dfrac{7\pi}{4}))\) is 
Let \(a,b,c,d \) be an increasing sequence of real numbers,which are in geometric progression .If \(a+d=112\) and \(b+c=48\) ,then the value of \(\dfrac{a+c+8}{b}\) is 
If \(y=x^{e^x}+x^{e} for x>0\),the  \( \dfrac{dy}{dx}\) is equal to ?
Suppose the line joining distinct points P and Q on \((x-2)^{2}+(y-1)^{2}=r^{2}\) is the diameter of \( (x-1)^2+(y-3)^2=4\).The value of r is 
If (2,-6),(5,2) and (-2,2) constitute the vertices of a triangle then the the line joining the origin and its orthocentre is